2.7. Syntax Arithmetic

2.7.1. Arithmetic Operators

  • + - Addition

  • - - Subtraction

  • * - Multiplication

  • / - Division

>>> 10 + 2
12
>>>
>>> 10 - 2
8
>>>
>>> 10 * 2
20
>>>
>>> 10 / 2
5.0

>>> x = 10
>>> y = 2
>>>
>>> x + y
12

2.7.2. Power and Root

  • a ** b - b power of the number a

  • a ** (1/b) - b-th root of the number a

>>> 10 ** 2
100
>>>
>>> 2 ** -1
0.5
>>>
>>> 1.337 ** 3
2.389979753

>>> 4 ** (1/2)
2.0
>>>
>>> 2 ** (1/2)
1.4142135623730951
>>>
>>> 27 ** (1/3)
3.0

>>> 4 ** 0.5
2.0
>>>
>>> 2 ** 0.5
1.4142135623730951
>>>
>>> 27 ** 0.333
2.9967059728946346

2.7.3. Divisions

There are three (and even four if counting divmod) ways of dividing numbers in Python:

  • / - True Division (changes type to float)

  • // - Floor division (preserving data type)

  • % - Modulo division (reminder)

The most common is true division, which changes type to float to preserve mathematical correctness:

>>> 12 / 6
2.0
>>>
>>> 12 / 5
2.4

Note, that the floor division preserves types, so it is more correct in computer science way. However it will produce invalid values from math perspective:

>>> 12 // 6
2
>>>
>>> 12 // 5
2

There is also a modulo division, which is more frequently used than you might think. Modulo division is the reminder from true division:

>>> 12 % 6
0
>>>
>>> 12 % 5
2

2.7.4. Parity Check

Modulo division is most frequently used to test if value is even or odd. In such case, you need to modulo divide number by 2 and check the reminder. If the reminder is 0, than the original number was even, if the reminder is false, the original number was odd:

>>> 10 % 2
0
>>>
>>> 11 % 2
1
>>>
>>> 12 % 2
0
>>>
>>> 13 % 2
1

>>> 10 % 2 == 0
True
>>>
>>> 11 % 2 == 0
False
>>>
>>> 12 % 2 == 0
True
>>>
>>> 13 % 2 == 0
False

2.7.5. Operator Precedence

  • Python uses mathematical operator precedence

  • More information in Boolean Operators.

>>> 1+2 * 3
7

>>> (1+2) * 3
9